Usage

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Arguments

xyORdist

Either a matrix of spatial coordinates or a distance matrix
(class dist).

thresh

A threshold value for truncation of the geographic distance
matrix. If thresh=NULL, the length of the longest edge of the minimum
spanning tree will be used as the threshold (as returned by the function
give.thresh).

MEM.autocor

A string indicating if all MEMs must be returned or only
those corresponding to non-null, positive or negative autocorrelation. The
difference between options all and non-null is the following:
when there are several null eigenvalues, option all removes only one
of the eigenvectors with null eigenvalues and returns (n-1) eigenvectors,
whereas non-null does not return any of the eigenvectors with null
eigenvalues. Default: MEM.autocor="positive".

store.listw

A logical indicating if the spatial weighting matrix should
be stored in the attribute listw of the returned object

silent

A logical indicating if some information should be printed
during computation: truncation level and time to compute the dbmem

Details

dbMEM eigenfunctions were called PCNM in early papers (Borcard and
Legendre 2002, Borcard et al. 2004). There is a small difference in the
computation: to construct PCNMs, the distance matrix subjected to PCoA
contained zeros on the diagonal. In dbMEM, the matrix contains 4*thresh
values on the diagonal. The result is that the dbMEM eigenvalues are smaller
than the PCNM eigenvalues by a constant (equal to (n.sites *
(4*thresh)^2)/2). The dbMEM eigenvalues are proportional to Moran's I
coefficient of spatial correlation (Dray et al. 2006; Legendre and Legendre
2012). The dbMEM eigenvectors only differ from the PCNM eigenvectors by a
multiplicative constant; this has no impact on the use of MEMs as
explanatory variables in linear models. In this implementation, dbMEM
eigenvectors have a norm equal to 1 (using the uniform weigts 1/n.sites).

If a truncation value is not provided, the largest distance in a minimum
spanning tree linking all sites on the map is computed (returned by the
function give.thresh). That value is used as the truncation threshold
value (thresh).

A square regular grid produces multiple eigenvalues (i.e. eigenvalues that
are equal) and multiple eigenvalues have an infinity of eigenvector
solutions. Hence, different eigenvectors may be produced by this function on
computers with different operating systems or implementations of R. In
addition, the eigenvectors found by the dbmem function from the site
coordinates may differ from the eigenvectors computed from the geographic
distance matrix among the sites. Nonetheless, the different complete sets of
eigenvectors will have the exact same explanatory power (R-square) for a
given response vector or matrix, despite the fact that they are not fully
correlated on a one-to-one basis. This is, however, not the case for subsets
of eigenvectors selected using stepwise procedures.

Value

An object of class orthobasisSp , subclass orthobasis.
The dbMEM eigenfunctions (principal coordinates of the truncated distance
matrix) are stored as a data.frame. It contains several attributes
(see ?attributes) including: